Known mechanical computer mice have been specified to have a resolution of 400 dots per inch (dpi) and a maximum speed of 5 inches per second (ips), and may be tested before shipping to 7 ips. Some optical sensors within optical computer mice may be specified as having the same resolution as mechanical computer mice, but are capable of much higher speeds, such as speeds greater than 50 ips. In prior computer mice (both mechanical and optical), the resolution and speed limits imply that no more than 7 bits of magnitude are needed to transmit the number of dots (Δx, Δy) counted during sampling intervals. For example, values from 0 through 127 can be represented in a 7 bit value and values in the range of −128 through 127 can be represented by a two's-complement value in 8 bits (a 7 bit magnitude and a sign bit).
One particular prior art optical wireless computer mouse appears to send an 8 bit signed value (using a resolution of 800 dpi), indicating an amount of movement in each of a horizontal and vertical direction, via a Radio Frequency (RF) packet every 20 milliseconds. This would yield a maximum mouse speed of about 8 ips. (50 RF packets per second (20 millisecond time intervals)×127 (maximum signed 8 bit value)×0.00125 inches per dot (800 dpi resolution)=7.9375 inches per second). Using a resolution of 400 dpi would yield a maximum speed of about 16 ips; however, the maximum tracking speed that a low speed USB device can support is 36 ips (at a 400 dpi resolution).
A ten-fold increase in speed, as may be attained by an optical mouse, means that the Δx, Δy data could have a magnitude up to ten times larger than the magnitude for prior art mechanical mice. Therefore, 4 additional bits, or 11 bits would be required to report such a magnitude and 12 bits would be required to report the 11 bit magnitude and a sign bit. Since the smallest unit of addressable memory is a byte, an additional byte of memory would be required to accommodate the additional bits for reporting such a large magnitude. Given that available memory, such as Random Access Memory (RAM), is limited, a means for reporting such a large magnitude without using additional bits to represent the magnitude would be desirable.